topology matching for fully automatic similarity matching of 3d shapes masaki hilaga yoshihisa...
Post on 15-Jan-2016
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Topology Matching For Fully Automatic Similarity
Matching of 3D Shapes
Masaki HilagaYoshihisa ShinagawaTaku KohmuraTosiyasu L. Kunii
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Shape Matching Problem Similarity between
3D objects Metric near-
invariants Rigid transformations Surface simplification Noise
Fast
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Technique (1) Construct Multiresolution
Reeb Graph (MRG) normalized geodesic
distanceGeodesic distance function
Multiresolution Reeb Graph
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Technique (2) MRG matching algorithm
for similarity queries Finds most similar regions
Most similar regions on two frogsMatching nodes of two MRGs
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Reeb Graph
Same as in Chand’s presentation Can use any function
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Geodesic distance function Integral of geodesic
distances (v) = p g(v,p) dS
Normalize n(v) = ((v) – min())
/ min()
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Geodesic Approximation Approximate integral
Sample Simplify distance Use Dijkstra’s
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Multiresolution Reeb Graph Binary discretization Preserve parent-child relationships Exploit them for matching
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Matching process Calculate
similarity Match nodes
Find pairs with maximal similarity
Preserve multires hierarchy topology
Sum up similarity
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Matching Process
R S Match if:
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Matching Process
R S Match if:
Same height range
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Matching Process
R S Match if:
Same height range
Parents match
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Matching Process
R S Match if:
Same height range
Parents match
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Matching Process
R S Match if:
Same height range
Parents match
Match on graph path
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Results Invariants satisfied
fairly well Between pairs,
similarity 0.94 Across pairs,
similarity 0.76
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Results Database, 7 levels of MRG Similarity calculated in tens of milliseconds Database searched in average ~10 seconds
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Critique Subjectively good
matching Meet invariance criteria
Approximation of geodesic distance
Reeb graph discretization All models in DB must
have same parameters Similarity metric